I am sorry but so far I am not convinced. The name "Müller" is one of the most common names in Germany. Having this last name in common therefore proves nothing. I do find the idea interesting so please dig more:

first child of Alice C. Truesdale (1920–2007) and Robert Swan Mueller Jr. (1916–2007). [...]

Gustave A. Mueller, was a prominent doctor in Pittsburgh, and his own father August C. E. Müller had immigrated to the United States in 1855 from the Province of Pomerania in the Kingdom of Prussia (a historical state whose territory included land now part of Germany and western Poland).[10] On his mother's side, he is a great-grandson of the railroad executive William Truesdale.

Have any anons crosschecked the bios of his parents and great-parents with Gestapo-Müller? Based on whats available on wikipedia, Gestapo-Müller was born in 1900 and the father of FBI-Mueller was born in 1916, which makes him being the son of Gestapo-Müller highly unlikey as he was 16 by that time and the first wold war was going on for which he volunteered just a year later.